Texture Classification Using Rao’s Distance on the Space of Covariance Matrices

  • Salem Said
  • Lionel BombrunEmail author
  • Yannick Berthoumieu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9389)


The current paper introduces new prior distributions on the zero-mean multivariate Gaussian model, with the aim of applying them to the classification of covariance matrices populations. These new prior distributions are entirely based on the Riemannian geometry of the multivariate Gaussian model. More precisely, the proposed Riemannian Gaussian distribution has two parameters, the centre of mass \(\bar{Y}\) and the dispersion parameter \(\sigma \). Its density with respect to Riemannian volume is proportional to \(\exp (-d^2(Y; \bar{Y}))\), where \(d^2(Y; \bar{Y})\) is the square of Rao’s Riemannian distance. We derive its maximum likelihood estimators and propose an experiment on the VisTex database for the classification of texture images.


Texture classification Information geometry Riemannian centre of mass Mixture estimation EM algorithm 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Salem Said
    • 1
  • Lionel Bombrun
    • 1
    Email author
  • Yannick Berthoumieu
    • 1
  1. 1.Laboratoire IMS, CNRS - UMR 5218Université de BordeauxBordeauxFrance

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